Analysis of Linear Sequential Circuits by Confluence Sets

In this paper the group-theoretical concept of ``confluence sets´´ is introduced as a valuable tool in the analysis of linear sequential circuits (LSC´s). Using this concept, a scheme is formulated for producing state graphs of autonomous LSC´s which, in the ``singular´´ case, is superior to currently known schemes. Singular LSC´s, which are of potential interest in error correction systems, are studied in detail. Properties of their state graphs are derived, culminating in a unique characterization of such graphs in terms of representative ``cycles´´ and ``trees.´´ Together with known results on nonsingular circuits, the results in this paper offer a description of the autonomous behavior of the general linear sequential circuit.